Structure%20and%20Motion

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Structure and Motion

• Jean-Claude LatombeComputer Science Department
  Stanford University
• NSF-ITR Meeting on

November 14, 2002
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Stanfords Participants

• PIs L. Guibas, J.C. Latombe, M. Levitt
• Research Associate P. Koehl
• Postdocs F. Schwarzer, A. Zomorodian
• Graduate students S. Apaydin (EE), S. Ieong
  (CS), R. Kolodny (CS), I. Lotan (CS), A. Nguyen
  (Sc. Comp.), D. Russel (CS), R. Singh (CS), C.
  Varma (CS)
• Undergraduate students J. Greenberg (CS),E.
  Berger (CS)
• Collaborating faculty
• A. Brunger (Molecular Cellular Physiology)
• D. Brutlag (Biochemistry)
• D. Donoho (Statistics)
• J. Milgram (Math)
• V. Pande (Chemistry)

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Problems Addressed

• Biological functions derive from the structures
  (shapes) achieved by molecules through motions
• ? Determination, classification, and
  prediction of 3D protein structures
• ? Modeling of molecular energy and
  simulation of folding and binding motion

4
Whats New for Computer Science?

• Massive amount of experimental data
• Importance of similarities
• Multiple representations of structure
• Continuous energy functions
• Many objects forming deformable chains
• Many degrees of freedom
• Ensemble properties of pathways

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Massive amount of experimental data

• ? Abstract/simplify data sets into compact data
  structures

E.g. Electron density map ? Medial axis
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Importance of similarities

• ?Segmentation/matching/scoring techniques

E.g. Libraries of protein fragmentsKolodny,
Koehl, Guibas, Levitt, JMB (2002)
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1tim Approximations
real protein
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Alignment of Structural Motifs Singh and Saha
Kolodny and Linial

• Problem
• Determine if two structures share common motifs
• 2 (labelled) structures in R3 Aa1,a2,,an,
  Bb1,b2,,bm
• Find subsequences sa and sb s.t the
  substructures asa(1),asa(2),,
  asa(l) bsb(1),bsb(2),, bsb(l) are similar
• Twofold problem alignment and correspondence
• Score ?? Approximation ?? Complexity

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R. Singh and M. Saha. Identifying Structural
Motifs in Proteins.Pacific Symp. on
Biocomputing, Jan. 2003.
Iterative Closest Point (Besl-McKay) for
alignment
? Score RMSD distance
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R. Singh and M. Saha. Identifying Structural
Motifs in Proteins.Pacific Symp. on
Biocomputing, Jan. 2003.
Trypsin
Trypsinactivesite
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R. Singh and M. Saha. Identifying Structural
Motifs in Proteins.Pacific Symp. on
Biocomputing, Jan. 2003.
Trypsin active site against 42Trypsin like
proteins
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Multiple representations of structure

ProShape softwareKoehl, Levitt
(Stanford),Edelsbrunner (Duke)
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Statistical potentials for proteins based on
alpha complex Guibas, Koehl, Zomorodian

• Decoys generated using physical potentials
• Select best decoys using distance information

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• Continuous energy functions
• Many objects in deformable chains

• ?Many pairs of objects, but relatively few are
  close enough to interact
• ? Data structures that capture proximity, but
  undergo small or rare changes

During motion simulation - detect steric clashes
(self-collisions) - find pairs of atoms closer
than cutoff
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• Other application domains
• Modular reconfigurable robots
• Reconstructive surgery

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• Fixed Bounding-Volume hierarchies dont work

sec17
17

• Instead, exploit what doesnt change chain
  topology? Adaptive BV hierarchiesGuibas,
  Nguyen, Russel, Zhang Lotan, Schwarzer,
  Halperin, Latombe (SOCG02)

sec17
18

• Wrapped bounding sphere hierarchiesGuibas,
  Nguyen, Russel, Zhang (SoCG 2002)

• WBSH undergoes small number of changes
• Self-collision
• O(n logn ) in R2 O(n2-2/d) in Rd, d ? 3

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• ChainTreesLotan, Schwarzer, Halperin, Latombe
  (SoCG02)

Assumption Few degrees of freedom change at each
motion step (e.g., Monte Carlo simulation)

• Find all pairs of atoms closer than a given
  cutoff
• Find which energy terms can be reused

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• ChainTreesLotan, Schwarzer, Halperin, Latombe
  (SoCG02)

Updating
Finding interacting pairs
(in practice, sublinear)
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• ChainTreesApplication to MC simulation
  (comparison to grid method)

m1
m 5
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• Future work ChainTrees

• Run new series of experiments with more complex
  energy field EEF1 Lazaridis Karplus
  (with Pande)
• Use library of fragments (with Koehl)

Open problem How to find good moves to make when
the conformation is compact and random moves are
rejected with high probability?
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• Future Work Spanner for deformable
  chainAgarwal, Gao, Duke Nguyen, Zhang,
  Stanford

3HVT
Capture proximity information with a sparse
spanner
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Many degrees of freedom

• ?Tools to explore large dimensional conformation
  space
• - Sampling strategies - Nearest neighbors

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Sampling structures by combining
fragmentsKolodny, Levitt
Library of protein fragments
? Discrete set of candidate structures
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Nearest neighbors in high-dimensional
spaceLotan and Schwarzer
Find k nearest neighbors of a given protein
conformation in a set of n conformations (cRMS,
dRMS)
Idea Cut backbone into m equal subsequences
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Nearest neighbors in high-dimensional
spaceLotan and Schwarzer
100,000 decoys of 1CTF (Park-Levitt
set) Computation of 100 NN of each conformation
Full rep., dRMS (brute force) 84h
Ave. rep., dRMS (brute force) 4.8h
SVD red. rep., dRMS (brute force) 41min
SVD red. rep., dRMS (kd-tree) 19min
80 of computed NNs are true NNskd-tree
software from ANN library (U. Maryland)
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Ensemble properties of pathways

• ? Stochastic nature of molecular motion requires
  characterizing average properties of many
  pathways

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Example 1 Probability of Folding pfold
We stress that we do not suggest using pfold as
a transition coordinate for practical purposes as
it is very computationally intensive. Du,
Pande, Grosberg, Tanaka, and Shakhnovich On the
Transition Coordinate for Protein Folding
Journal of Chemical Physics (1998).
Folded set
Unfolded set
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Example 2 Ligand-Protein InteractionSept,
Elcock and McCammon 99
10K to 30K independent simulations
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Probabilistic Roadmap Apaydin, Brutlag, Hsu,
Guestrin, Latombe (RECOMB02, ECCB02) Idea
Capture the stochastic nature of molecular motion
by a network of randomly selected conformations
and by assigning probabilities to edges
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Probabilistic Roadmap Apaydin, Brutlag, Hsu,
Guestrin, Latombe (RECOMB02, ECCB02)

• One linear equation per node
• Solution gives pfold for all nodes
• No explicit simulation run
• All pathways are taken into account
• Sparse linear system

l
k
j
Pik
Pil
Pij
m
Pim
i
Pii
Let fi pfold(i) After one step fi Pii fi
Pij fj Pik fk Pil fl Pim fm
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Probabilistic Roadmap
Correlation with MC Approach

• 1ROP (repressor of primer)
• 2 a helices
• 6 DOF

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Probabilistic Roadmap
Computation Times (1ROP)
Monte Carlo
Over 106 energy computations
Over 11 days of computer time
49 conformations
Roadmap
15,000 energy computations
1 - 1.5 hours of computer time
5000 conformations
4 orders of magnitude speedup!
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Future work Probabilistic Roadmap

• Non-uniform sampling strategies
• Encoding molecular dynamics into probabilistic
  roadmaps (with V. Pande)
• Quantitative experiments with ligand-protein
  binding (with V. Pande)

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Bio-X Clark Center
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The following slides relate to non-research
issues. I do not plan to present them. Jack and
Leo may want to use the contents of some of them
for their own presentations.
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Education

• Tutorial on Delaunay, Alpha-Shape and Pockets
  (Koehl)
• A biocomputing Notebook (Koehl)
• Biocomputation lectures in pre-existing classes
• CS326 motion planning molecular motion,
  probabilistic roadmaps, self-collision detection
  (Latombe)
• CS468 intro to computational topology finding
  pockets and tunnels in molecules, compute surface
  areas and volumes and their derivative
  (Zomorodian)
• New class on Algorithmic Biology (Batzoglu,
  Guibas, Latombe)
• Graduate Curriculum Committee, Bio-Engineering
  Dept., Stanford (Latombe)

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Trained Students (1/2)

• PhD students
• Serkan Apaydin, EE
• An Nguyen, Scientific Computing
• Carlos Guestrin, CS (Daphne Kollers group)
• Itay Lotan, CS
• Rachel Kolodny, CS
• Daniel Russel, CS
• Samuel Ieong, CS

Most graduate students have a principal advisor
in CS and a secondaryone in a bio-related
department (Levitt, Brutlag, Pande)
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Trained Students (2/2)

• Graduated Master students
• Rohit Singh, finding motifs in proteins, best
  Stanford CS masters thesis, June 02 current
  position bioinformatics company in San Diego
• Chris Varma, study of ligand-protein interaction
  with probabilistic roadmaps, June 02 current
  position PhD student, Harvard/MIT Biomedical
  program
• Current Master student
• Ben Wong, modeling T cell activity
• Undergraduate
• Eric Berger, CS, Stanford, summer internship
• Julie Greeberg, CS, Harvard, summer internship

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Visitors

• Prof. Alberto MunozMath Dept., University of
  Yucatan, Mexico3 months, Summer02Haptic
  interaction and probabilistic roadmaps
• Prof. Ileana StreinuSmith College6 months, from
  Sept.02Protein folding

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Interactions Within Stanford

• - Guibas and Levitt, with J. Milgram (Math)
  topology of configuration spaces of chains-
  Guibas, with V. Pande (Chemistry) and D. Donoho
  (Statistics) non-linear multi-resolution analysis
  of molecular motions- Latombe and Apaydin, with
  D. Brutlag (Biochemistry) and V. Pande
  probabilistic roadmaps- Latombe and Lotan with
  V. Pande efficient MC simulation

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Interactions Outside Stanford

• - Collision Detection for Deforming Necklaces,
  P. Agarwal, L. Guibas, A. Nguyen, D. Russel, and
  L. Zhang. Invited to special issue of Comp.
  Geom., Theory and Applications, following
  presentation at SoCG'02.- Kinetic Medians and
  kd-Trees, P. Agarwal, J. Gao, and L. Guibas.
  Proc. 10th European Symp. Algorithms, LNCS 2461,
  Springer-Verlag, 5-16, 2002.- Stochastic Roadmap
  Simulation An Efficient Representation and
  Algorithm for Analyzing Molecular Motion, M.S.
  Apaydin, D.L. Brutlag, C. Guestrin, D. Hsu, and
  J.C. Latombe. Proc. RECOMB'02, Washington D.C.,
  pp. 12-21, 2002. - Efficient Maintenance and
  Self-Collision testing for Kinematic Chains, I.
  Lotan, F. Schwarzer, D. Halperin, and J.C.
  Latombe, SoCG02, pp. 43-42. June 2002.-
  Stochastic Conformational Roadmaps for Computing
  Ensemble Properties of Molecular Motion, M.S.
  Apaydin, D.L. Brutlag, C. Guestrin, D. Hsu, and
  J.C. Latombe. Workshop on Algorithmic Foundations
  of Robotics (WAFR), Nice, Dec. 2002.

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Attendance to Conferences

• - BCATS 01 and 02 Bio-Computation At
  Stanford- RECOMB 02 Int. Conf. on Research in
  Computational Biology- ISMB 02 Int. Conf. on
  Intelligent Syst. for Molecular Biology- ECCB
  2002 European Conf. on Computational Biology-
  Biophysical Society Symp. on Molecular
  Simulations in Structural Biology, 2002- SoCG
  2002 ACM Symp. on Computational Heometry

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Outreach

• - Latombe and Levitt serve as members of the
  Scientific Leadership Council of Stanfords
  Bio-X program- Presentations Stanfords Bio-X
  Symposium (3/02), Stanfords Computer Forum
  (3/02), Berkeleys Broad Area Seminar (4/02)-
  Conference committees Guibas, program
  committee, WAFR02 and SoCG03 Latombe,
  program committee, 1st IEEE Bioinformatics Conf.
  03 Apaydin, organization committee of BCATS02

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The following slides are extra slides that I
removed from my presentation for lack of time
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General Goals

• Larger proteins considered ? computational
  efficiency
• Diversity of molecules and interactions ?
  computational abstractions
• Extension of in-silico experiments ?
  computational correctness
• ?Enable biological studies that were not
  possible before, more systematically

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Approach

• Select hard problems
• Close interaction between computer scientists
  (Guibas, Koehl, Latombe) and biologists (Koehl,
  Levitt, Brutlag, Pande, Brunger)
• Most graduate students are CS students with
  secondary advisor in biology
• Perform extensive tests

49

• Electron density map ? Medial axisGuibas,
  Brunger, Russel
• Medial axis of iso-surfaces to estimate backbone
• Cleaning and simplification of axis to filter
  noise out
• Persistence of features across multiple
  iso-surfaces

sec17
50
Continuous energy function

• ?Essential for protein structure prediction and
  molecular motion simulation
• - Statistical potentials based on alpha
  complex
• - Maintenance of energy values during
  simulation

51

• Instead, exploit what doesnt change chain
  topology? Adaptive BV hierarchies
• Balanced binary trees of constant topology
• Efficient repair of position/size of BVsGuibas,
  Nguyen, Russel, Zhang Lotan, Schwarzer,
  Halperin, Latombe (SOCG02)

sec17
52

• Future WorkSpanner for deformable
  chainAgarwal, Gao, Duke Nguyen, Zhang,
  Stanford

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Probabilistic Roadmap

• 1ROP (repressor of primer)
• 2 a helices
• 6 DOF

• 1HDD (Engrailed homeodomain)
• 3 a helices
• 12 DOF

H-P energy model with steric clash exclusion Sun
et al., 95